If r is a linear function with a slope that is not equal to zero, which of the following is always true of its inverse function?
Its slope is the negative reciprocal of the slope of r.
Its slope is the reciprocal of the slope of r.
Its y-intercept is the negative reciprocal of the y-intercept of r.
Its y-intercept is the reciprocal of the y-intercept of r.

Question

If r is a linear function with a slope that is not equal to zero, which of the following is always true of its inverse function?
Its slope is the negative reciprocal of the slope of r.
Its slope is the reciprocal of the slope of r.
Its y-intercept is the negative reciprocal of the y-intercept of r.
Its y-intercept is the reciprocal of the y-intercept of r.

ericthestein · Answer

Its slope is the reciprocal of the slope of r

This is because an inverse function basically switches the y-value with the x-value. If you had $$y = \frac{ -1 }{ 3 }x + 1$$
the inverse function would be
$$x = \frac{ -1 }{ 3 }y + 1$$
Then it's just a matter of solving for y. Do so and you'll get $$y = -3x + 3$$
Because -3 is the reciprocal of -1/3 (flip the fraction and you'll get -3/1 = -3), and because none of the other answer choices are true, the answer is B.